**Diploma Strength of Materials Important Formulas**

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Unit 1 ENGINEERING MATERIALS

Chapter: 1.1: Engineering materials: Classification – definition of Mechanical properties – ferrous metals – cast iron – uses – advantages – types of cast iron – properties and applications – effect of impurities on cast iron. steel – classification – alloying elements – purpose of alloying – effect of alloying elements on steel – uses of steels – properties of mild steel – defects in steel – applications – properties of hard steel – market forms of steels – nonferrous metals – properties and uses.

Chapter: 1.2: Mechanical testing of materials:

Compression test – bend test – hardness test – Brinell hardness test, Vickers hardness test, Rockwell hardness test – impact test – fatigue test creep test. Tensile test of mild steel in UTM – stress strain diagram – limit of proportionality – elastic limit – yield stress – breaking stress – ultimate stress – percentage of an elongation and percentage reduction in area – problems.

Chapter: 1.3: Friction

Introduction – definition – force of friction – limiting friction – static friction – dynamic friction – angle of friction – coefficient of friction – laws of static and dynamic friction. Description only.

DEFORMATION OF METALS

Chapter: 2.1: Simple stresses and strains

Definition – load, stress and strain – classification of force systems: tensile, compressive and shear force systems. Hooke’s law – definition Young’s modulus – working stress, factor of safety, load factor, shear stress and shear strain – modulus of rigidity. Linear strain – deformation due to tension and compressive forces – simple problems in tension, compression and shear forces.

Chapter: 2.2: Elastic constants

Definition – lateral strain – poison’s ratio – volumetric strain – bulk modulus – volumetric strain of rectangular and circular bars – problems connecting linear, lateral and volumetric deformations – elastic constants and their relationship – problems on elastic constants. Composite bar – definition – problems in composite bars subjected to tension and compression. Temperature stresses and strains – simple problems.

Chapter: 2.3 Strain Energy

Definition – proof resilience – modulus of resilience – the expression for strain energy stored in a bar due to axial load – instatntaneous stresses due to gradual, sudden, impact and shock loads – problems computing instantaneous stress and deformation in gradual, sudden, impact and shock loadings

GEOMETRICAL PROPERTIES OF SECTIONS AND THIN SHELLS

Chapter: 3.1: Properties of sections

Definition – center of gravity and centroid – position of centroids of plane

geometrical figures such as rectangle, triangle, circle and trapeziumproblems to determine the centroid of angle, channel, T and I sections only – Definition – centroidal axis parallel axis theorem and perpendicular axis theorem (

Moment of Inertia of lamina of rectangle, circle, triangle, I and channel

sections – Definition Problems computing moment of inertia and radius of gyration for angle, T, Channel and I section

Chapter: 3.2: Thin Shells

Definition – Thin and thick cylindrical shell shell subjected to internal pressure stress causes in a thin cylindrical shell subjected to internal pressure simple problems –

subjected to internal pressure induced in a thin spherical shell subjected to internal pressure problems – change in diameter and volume o to internal pressure –

IV THEORY OF TORSION AND SPRINGS

Chapter: 4.1: Theory of Torsion

Assumptions – torsion equation hollow shafts – power transmitted Torsional rigidity –

hollow and solid shafts in weight and strength considerations Advantages of hollow shafts over solid shafts

Chapter: 4.2: Springs

Types of springs – Difference between open and closely coiled helical springs

coiled helical spring subjected to an axial load shear stress, deflection, stiffness and resilience of closed coiled helical springs.

V SF AND BM DIAGRAMS OF BEAMS AND THEORY OF BENDINGChapter:

5.1: SF and BM diagrams

Classification of beams sign conventions for shear force and bending moment

loadings – Relationship between load, force and bending moment at a section – shear force diagram and bending moment diagram of cantilever and simply supported beam subjected to point load and uniformly distributed load (UDL) – Determination of Maximum bending moment in cantilever beam and simply supported beam when they are subjected to point load and uniformly distributed load.

Chapter: 5.2: Theory of bending

Theory of simple bending – Assumptions – Neutral axis – bending stress distribution – moment of resistance – bending equation – M/I=f/y=E/R – Definition – section modulus – rectangular and circular sections – strength of beam – simple problems involving flexural formula for cantilever and simply supported beam.

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